What makes Google Translate fail on the Latin language?
I don't know what model Google is using for their translations, but it's highly likely that they're using one of today's SOTA deep learning models.
The latest NLP models are trained on data scraped from the web, e.g. OpenAI's GPT-2 was trained on a dataset of 8 million web pages, Google's BERT was trained on the BookCorpus (800M words) and English Wikipedia (2.500M words) pages.
Now think about the amount of latin web pages and notice that there are over 6 million english wikipedia articles but less than 135.000 in latin (see here).
As you can see, massive amounts of data are crucial for neural machine translation and I assume there is simply not enough out there for latin. Plus latin is one of the most complex and complicated languages, this makes the task not easier. Maybe Google and Co also focus less on a 'dead' language which is not spoken anymore and has it's right to exist more for educational purposes.